Prime Detective

What your child will figure out

• Test whether a number has an exact factor and use the product as visible evidence.
• Classify primes, composites, perfect squares, and semiprimes from complete factor evidence rather than appearance.
• Build every factor pair without duplicates and test unfamiliar numbers efficiently by stopping at the square root.
• Use a sieve to remove multiples and reveal the primes that remain.

The levels

1. The case of 12

   Predict and test a multiplication pair, then observe that an exact product exposes factors of 12.

2. The lonely 13

   Test possible divisors through √13 and explain why only 1 and 13 makes the number prime.

3. 18's full dossier

   Build all three factor pairs for 18 and stop when the pairs would repeat.

4. The odd-number alibi

   Disprove the idea that every odd number is prime by finding the structure of 21.

5. The square-root trap

   Include the square-root boundary when testing the perfect square 49.

6. The citywide sieve

   Transfer factor reasoning to a 2–30 sieve, remove multiples, and identify 29 from the survivors.

7. The missing multiple

   Find a less-familiar factor pair for 77 and see that composites need not match easy divisibility endings.

8. The crowded dossier

   Build all five factor pairs of 36, including the repeated square pair, without duplicates.

9. The long stakeout

   Test only prime divisors through √97 and stop once the search is complete.

10. The repeated fingerprint

    Recognize 121 as a perfect square whose decisive factor appears at the boundary.

11. The two-prime conspiracy

    Expose 143 as a semiprime even though familiar small divisors fail.

12. The final deduction

    Transfer the shortest complete prime test independently to 157.